For the 1st year of life, breastmilk or Formula is a baby's PRIMARY source of nutrition. NOT solids and NOT other liquids. And to feed on-demand. ie: the breastmilk or formula.
6 months is also a growth-spurt time and a time of MANY developmental changes. Thus, they need to feed more often, more frequently and more. Thus, you cannot feed according to a 'schedule.' Because scheduled feedings does not keep up with baby.
Always, give the bottle BEFORE solids. Formula or breastmillk, is a baby's primary source of nutrition and calories. Not solids.
At this age, solids is only an introduction to 'eating.' Not their main intake nor meals.
Napping should be when he is tired. Not by a 'schedule.' It needs to go by his cues. Otherwise, a baby will get over-tired. And when over-tired, babies/kids actually sleep/nap worse and fall asleep worse.
And yes, a baby typically does get tired and needs a nap, after being awake for 2 hours. Even a bath at this age is an 'activity' for them.
My son, for the 1st year, napped 3 times a day, for at least 2 hours. I went by his cues. I knew him and when he gets tired. I always nursed him before naps and after. And on-demand at any time. My son, had a GINORMOUS appetite, was a big tall solid boy, nursed often, even if he was on solids once a day at this age. I nursed him on-demand 24/7, day and night. And he was in the 97th percentiles for growth. And grew like a weed. At growth-spurts, he nursed a TON and often. Which is normal.
You need to give him more bottles. And on-demand.
Often times, a baby will even need to feed every single hour. This is called "cluster feeding." And when they are having growth-spurts and developmental changes. Which 6 months old, is.
Also at this age, they can begin teething. This also tweaks their sleep.
Naps, for a baby, is not the same for all. There is no 'shoulds' that he should be taking 3 naps until 9 months old. I never heard of that. My son as I said, napped 3 times a day, for the 1st year. Then as he got closer to 2 years old, he napped 2 times a day. For 2 hours each. He is now 4 years old and STILL naps everyday, for at least 2 hours.
I go by his cues. And I know when he is tired. I don't put him to nap, when he is over-tired or past that window of tiredness.
When over-tired a baby/child has a harder time, napping and falling asleep and sleeping well.
Solids, will not 'make' him nap longer.
The focus should be on feeding him his Formula, not on giving him solids.
As I said, whether nursing or getting Formula, this is a baby's primary source of nutrition.